math 230 let f x y 2xyz i 3y 2 x 2 z j x 2 y k

Let F(x,y) = (2xyz)i + (3y 2 + x 2 z)j + (x 2 y)k

(i) Determine whether F is a conservative vector field.

(ii) Evaluate the line integral

R

C

F · dr where C is given by

C : r(t) = (1 + t)i + t 2 j + (2 − t)k, 0 ≤ t ≤ 6

 

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